The number of stereoisomers formed by the giv | vedclass

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(B) The given compound is $3,6$-dimethylpiperazine-$2,5$-dione. It contains $2$ chiral centers $(n=2)$. The molecule is symmetrical. The number of ste

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$3$

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(B) The given compound is $3,6$-dimethylpiperazine-$2,5$-dione. It contains $2$ chiral centers $(n=2)$. The molecule is symmetrical. The number of stereoisomers for a symmetrical molecule with an even number of chiral centers is given by the formula: $N = 2^{n-1} + 2^{(n/2)-1}$ Substituting $n=2$: $N = 2^{2-1} + 2^{(2/2)-1} = 2^1 + 2^0 = 2 + 1 = 3$. The $3$ stereoisomers are: $1$. $(R,R)$-isomer $2$. $(S,S)$-isomer $3$. $(R,S)$-meso isomer.

The number of stereoisomers formed by the given compound is

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